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A lot of Puranas talk about the creation of the universe after Sri Brahma is created (which is again different based upon different puranas). The puranas also talk about the life span of a Brahma deity.
So, is there any mention of previous or next Brahmas in the scriptures?
This chapter of the Shanti Parma of the Mahabharata describes how the Pancharatra tradition was passed down in seven different Mahakalpas. It also describes what part of Vishnu's body Brahma was born out of in each Mahakalpa, along with how each Brahma learned Pancharatra from Vishnu.
In that Kalpa when Brahma the Creator, O king, took his birth in the mind of Narayana and issued from the latter's mouth, Narayana himself performed, O Bharata, his Daiva and Paitra rites in accordance with this religion. Those Rishis that subsist upon the froth of water then obtained it from Narayana. From the froth-eating Rishis, this religion was obtained by those Rishis that go by the name of Vaikanasas. From the Vaikanasas, Shoma got it. Afterwards, it disappeared from the universe.
After the second birth of Brahma, viz., when he sprang from the eyes of Narayana, O king, the Grandsire (that is. Brahma) then received this religion from Shoma. Having received it thus, Brahma imparted this religion, which has Narayana for its soul, unto Rudra. In the Krita age of that ancient Kalpa, Rudra, devoted to Yoga, O monarch, communicated it to all those Rishis that are known by the name of Valikhilyas. Through the illusion of Narayana, it once more disappeared from the universe.
In the third birth of Brahma, which was due to the speech of Narayana, this religion once more sprang up, O king, from Narayana himself. Then a Rishi of the name of Suparna obtained it from that foremost of Beings. The Rishi Suparna used to recite this excellent religion, this foremost of cults, three times during the day. In consequence of this, it came to be called by the name of Trisauparna in the world. This religion has been referred to in the Rigveda. The duties it inculcates are exceedingly difficult of observance. From the Rishi Suparna, this eternal religion was obtained, O foremost of men, by the God of wind, that sustainer of the lives of all creatures in the universe. The God of wind communicated it unto such Rishis as subsist upon what remains of sacrificial offerings after feeding guests and others. From those Rishis this excellent religion was obtained by the Great Ocean. It once more disappeared from the universe and became merged into Narayana.
In the next birth of the high-souled Brahman when he Sprang from the ear of Narayana, listen, O chief of men, to what happened in that Kalpa. The illustrious Narayana, otherwise called Hari, when he resolved upon Creation, thought of a Being who would be puissant enough to create the universe. While thinking of this, a Being sprang from his ears competent to create the universe. The Lord of all called him by the name of Brahma. Addressing Brahma, the Supreme Narayana said unto him,--Do thou, O son, create all kinds of creatures from thy mouth and feet. O thou of excellent vows, I shall do what will be beneficial for thee, for I shall impart to thee both energy and strength sufficient to render thee competent for this task. Do thou receive also from me this excellent religion known by the name of Sattwata. Aided by that religion do thou create the Krita age and ordain it duly. Thus addressed, Brahma bowed his head unto the illustrious Hari, the god of the gods and received from him that foremost of all cults with all its mysteries and its abstract of details, together with the Aranyakas,--viz., that cult, which sprang from the mouth of Narayana. Narayana then instructed Brahma of immeasurable energy in that cult, and addressing him, said,--Thou art the creator of the duties that are to be observed in the respective Yugas. Having said this unto Brahma, Narayana disappeared and proceeded to that spot which is beyond the reach of Tamas, where the Unmanifest resides, and which is known by the men of acts without desire of fruits. After this, the boon-giving Brahma, the Grandsire of the worlds, created the different worlds with their mobile and immobile creatures. The age that first commenced was highly auspicious and came to be called by the name of Krita. In that age, the religion of Sattwa existed, pervading the entire universe. With the aid of that primeval religion of righteousness, Brahma, the Creator of all the worlds, worshipped the Lord of all the deities, viz., the puissant Narayana, otherwise called Hari. Then for the spread of that religion and desirous of benefiting the worlds, Brahman instructed that Manu who is known by the name of Swarochish in that cult. Swarochish-Manu, that Lord of all the worlds, that foremost of all persons endued with puissance, then cheerfully imparted the knowledge of that cult to his own son, O king, who was known by the name of Sankhapada. The son of Manu, viz., Sankhapada, communicated the knowledge of that to his own son Suvarnabha who was the Regent of the cardinal and subsidiary points of the compass. When, upon the expiration of the Kriti Yuga, the Treta came, that cult once more disappeared from the world.
In a subsequent birth of Brahman, O best of kings, viz., that which was derived from the nose of Narayana, O Bharata, the illustrious and puissant Narayana or Hari with eyes like lotus petals, himself sang this religion in the presence of Brahma. Then the son of Brahma, created by a fiat of his will, viz., Sanatkumara, studied this cult. From Sanatkumara, the Prajapati Virana, in the beginning of the Krita age, O tiger among Kurus, obtained this cult. Virana having studied it in this way, taught it to the ascetic Raivya. Raivya, in his turn, imparted it to his son of pure soul, good vows, and great intelligence, viz., Kukshi, that righteous Regent of the cardinal and subsidiary points of the compass. After this, that cult, born of the mouth of Narayana, once more disappeared from the world.
In the next birth of Brahma, viz., that which he was derived from an egg which sprang from Hari, this cult once more issued from the mouth of Narayana. It was received by Brahma, O king, and practised duly in all its details by him. Brahma then communicated it, O monarch, to those Rishis that are known by the name of Varhishada. From the Varhishadas it was obtained by a Brahmana well-versed in the Sama-Veda, and known by the name of Jeshthya. And because he was well-versed with the Samans, therefore was he known also by the name of Jeshthya-Samavrata Hari. From the Brahmana known by the name of Jeshthya, this cult was obtained by a king of the name of Avikampana. After this, that cult, derived from the puissant Hari, once more disappeared from the world.
During the seventh birth of Brahma due to the lotus, O king, that sprang from the navel of Narayana, this cult was once more declared by Narayana himself, unto the Grandsire of pure soul, the Creator of all the worlds, in the beginning of this Kalpa. The Grandsire gave it in days of yore to Daksha (one of his sons created by a fiat of his will). Daksha, in his turn, imparted it to the eldest of all the sons of his daughters, O monarch, viz., Aditya who is senior in age to Savitri. From Aditya, Vivaswat obtained it. In the beginning of the Treta Yuga, Vivaswat imparted the knowledge of this cult to Manu. Manu, for the protection and support of all the worlds, then gave it to his son Ikshaku. Promulgated by Ikshaku, that cult over-spreads the whole world. When the universal destruction comes, it will once more return to Narayana and be merged in Him. The religion which is followed and practised by the Yatis, has, O best of kings, been narrated to thee before this in the Hari Gita, with all its ordinances in brief. The celestial Rishi Narada got it from that Lord of universe, viz., Narayana himself, O king, with all its mysteries and abstract of details. Thus, O monarch, this foremost of cults is primeval and eternal. Incapable of being comprehended with ease and exceedingly difficult of being practised, it is always upheld by persons wedded to the attribute of Sattwa.
Whew! The Hari Gita, by the way, is another name for the Bhagavad Gita, and as the Mahabharata says it encapsulates the teachings of Pancharatra.
What we don't have, however, is information on who the Jivas were who became the Brahma in each Mahakalpa. But it's a common belief, though I don't know of a scriptural basis for it, that Hanuman will became the next Brahma. One person who believed it was Madhvacharya, who thought that it's because Hanuman is an incarnation of Vayu. Madhvacharya had an elaborate theory where the current Shiva becomes the next Vayu, the current Vayu becomes the next Brahma, and the current Brahma becomes the next Adiseshan. But I don't know of any scriptures that mention this.
Different names of Lord Brahma (during different Kalpas) are mentioned in this chapter of Skanda Purana:
Parvati curiously asked Lord Shiva about the reason why Somnath was known by so many different names. Lord Shiva said- ‘ Since the time this divine linga first manifested itself very few blessed souls had the knowledge of it’s existence. Brahma has a life span of one kalpa at the end of which even he ceases to exist giving way to his successor- a new Brahma. In the same manner this divine Linga acquires a new name at the end of each kalpa. The present kalpa is seventh in order as six kalpas have already passed. The name of the present Brahma is Shatanand and this divine Linga is presently famous by the name of Somnath. Similarly it was famous as Mrityunjay during the time of Brahma named Virinchi. During second kalpa this Linga was famous as Kalagnirudra and the name of Brahma was Padmabhu. The third kalpa had Swayambhu as Brahma and the Linga was famous as Amritesh. The name of the fourth Brahma was Parmeshthi in fourth kalpa and the linga was famous as Annamay. In the same way the names of the fifth and sixth Brahma were Surajyeshtha and Hemagarbha respectively and the names of the Linga during their periods were Kritiwas and Bhairav Nath respectively.’
